Question

Your leader wants you to evaluate the difference in cycle time between three different offices. Describe the steps you would take in the evaluation in order to provide a report so the leader can take action. Justify your response using what you learned from the topic materials. We learned about One-Way ANOVA and or w-TukeyKramer.

Answer 1

One-way analysis of variance (one-way ANOVA) is basically used to test the equality of population means when classification of observations is done by one variable only. Firstly there are some assumptions of one-way ANOVA :

(a) Populations from which samples are taken follow normal distribution. However if sample size is large, it automatically follows normal distribution.

(b) The sample observations should be random and independent.

(c) Populations from which samples are taken should have some variance,

(d) e_ij (effect due to chance) are independent and identically distributed

Now, we will talk about the steps taken to evaluate in order to provide the report.

For ANOVA we need firstly we need a null hypothesis and alternatie hypothesis.

Here it can be , H₀ : There is no significance difference in the average cycle time of three different offices.

H₁ : There is a significance difference in the average cycle time of three different offices.

Now we will have to collect the cycle times for all the three offices and then calculate the grand total and class total of the cycle time i.e.

X1	X2	X3	X12	X22	X32
x11	x21	x31	x112	x212	x312
....	....	....	....	....	....
x1a	x2b	x3c	x1a2	x2b2	x3c2
x1.= x11+...+x1a	x2.= x21+....+x2b	x3. = x31+....+x3c	x1.2= x112+...+x1a2	x2.2= x212+...+x2b2	x3.2= x312+...+x3c2

Now we need to find total sum of squares, Sum of squares between classes and degree of freedom.

Now grand total =  

Now Total Sum of Squares(TSS) =   

Here N = 3 X (No. of observations for the cycle time)

Now Sum of squares between classes(SST) =

Sum of squares due to error (SSE) = TSS - SST

Here the degree of freedom between classes will be 3-1 = 2 and due to error will be N-3.

Then we will have to calculate the mean sum of squares between classes (MST) and due to error (MSE)

MST = SST/2 and MSE = SSE/N-3

Now for F-ratio = SST/SSE.

After following all these steps you can make the report and then the leader can take the action.